First thoughts:
1. Is the house one-story or two-stories? If it's one-story, have you considered eliminating the window and installing a skylight in the middle of the kitchen?
2. A kitchen is not required by code to have a window. Yes, I know it's nice, but one option is to eliminate the window, even if you can't put in a skylight. It's possible to almost make up for the loss with really good kitchen lighting, consisting of under-cabinet task lighting, and over-cabinet ambient lighting, with no light source being visible, and by using certain types of lighting, color rendition will be excellent.
3. In a kitchen so small, when you remodel, keep the cabinets very light in color! Natural wood is lovely, but it's a light sponge, soaking up light, and giving a feeling of closing in on the occupants. Consider a couple, but not too many, of glass-door upper cabinets, which will lighten up the space and give a little bit more depth.
4. A small improvement would be cabinets above the refrigerator and range. Not terribly useful, but good for storing seldom-used items.
5. Ideally, there would be at least a small amount of counter on each side of the range. Keeps someone from bumping into overhanging pot handles and maybe spilling dinner. A foot is minimum, 18 inches is better.
6. The basic layout is good, refrigerator, sink and range are in the right places, and the family can get to the refigerator without entering the work triangle, so I wouldn't alter the basic layout at all.
7. The best hope for more cabinet space is the window wall. Opening up to the living room doesn't make much sense because it's the wall with the range on it...not terribly attractive from the rear, and you don't want grease and spills in the living room. You could, however, use a high upper cabinet like the one over your sink, and open the bit of wall between upper and lower cabinets to the living room, if you want some open-ness.
Those are my first reactions, and I don't think I can produce any miracles beyond that. It will give you some food for thought, and I'll watch this space for your reactions.
PS: Never even a thank you. Oh well.
Architect (NY) and Home Designer (PA)